FIG. 1A (prior art) is a representative view showing a partial plot of the helicoid plane known heretofore.
FIG. 1B (prior art) is a representative view of an inducer for centrifugal pumps having helicoid planar surfaces currently in use. As best shown in FIG. 1B, helicoid planar surfaces are commonly found in inducer blade configuration for centrifugal pump.
An inducer is an axial flow impeller with blades that wrap in a helix around a central hub or shaft. Inducers are commonly used in cryogenic systems, including storage tanks, rocket fuel pump feed systems, and other similar uses. Inducers are used in such systems to prevent the fluid being moved from cavitating in the impeller or pump, which can occur when there is not enough pressure to keep the liquid from vaporizing, at least in part. Noncavitating inducers are used to pressurize the flow of the input fluid sufficient to enable the devices to which the inducer is attached to operate efficiently. An excellent discussion of the fluid dynamic properties of inducers is provided by B. Lakshminarayana, Fluid Dynamics of Inducers—A Review, Transactions of the ASME Journal of Fluids Engineering, December 1982, Vol. 104, Pages 411-427, which is incorporated herein by reference.
In theory, the helicoid, derived from the plane and the catenoid, is the third minimal surface to be known. It was first discovered by Jean Baptiste Meusnier in 1776. Its name derives from its similarity to the helix: for every point on the helicoid there is a helix contained in the helicoid which passes through that point. Since it is considered that the planar range extends through negative and positive infinity, close observation shows the appearance of two parallel or mirror planes in the sense that if the slope of one plane is traced, the co-plane can be seen to be bypassed or skipped, though in actuality the co-plane is also traced from the opposite perspective.
The helicoid is also a ruled surface (and a right conoid), meaning that it is a trace of a line. Alternatively, for any point on the surface, there is a line on the surface passing through it. Indeed, Catalan proved in 1842 that the helicoid and the plane were the only ruled minimal surfaces.
The helicoid and the catenoid are parts of a family of helicoid-catenoid minimal surfaces.
The helicoid is shaped like Archimedes' screw, but extends infinitely in all directions. It can be described by the following parametric equations in Cartesian coordinates:x=ρ cos(αθ),y=ρ sin(αθ),z=θ, 
where ρ and θ range from negative infinity to positive infinity, while α is a constant. If α is positive then the helicoid is right-handed as shown in the figure; if negative then left-handed.
The helicoid has principal curvatures ±1/(1+ρ2). The sum of these quantities gives the mean curvature (zero since the helicoid is a minimal surface) and the product gives the Gaussian curvature.
The helicoid is homeomorphic to the 2. To see this, let alpha decrease continuously from its given value down to zero. Each intermediate value of α will describe a different helicoid, until α=0 is reached and the helicoid becomes a vertical plane.
Conversely, a plane can be turned into a helicoid by choosing a line, or axis, on the plane then twisting the plane around that axis.
FIG. 1C (prior art) is a representative view showing a partial plot of the helicoid plane surface of the inducer rotor currently in use.
FIG. 1D (prior art) is a representative view showing another partial plot of the helicoid plane surface and vertical bisecting plane of the inducer rotor currently in use.
FIG. 1E (prior art) is a representative view showing an axial water-jet pump 60 such as used for propulsion of a high-speed boat currently in use. As best shown in FIG. 1E, the inducer blades 61 rotate around the shaft 63 in direction A as they sweep through the water. The back side 62 of the blade pushes against the water, trying to accelerate it within the inducer passage, as the front side 64 of the blade experiences a localized reduction in pressure. As a result, water enters the inducer from the inlet 66 and gains rotational momentum while being pushed along the length of the inducer and eventually propelled out of the inducer at the outlet 68 in much higher speed after going through a stator 69 with counter-rotational blades which reduces the rotational momentum of the water, if any, and directs the water directly out the end 68 in direction B.
A common problem with spiral or helical inducers used within centrifugal pumps and similar devices is that the fluid in the tank in which the centrifugal pump is installed will begin to rotate in the same direction as, and along with, the inducer blades. When this occurs, the fluid does not move up through the inducer as efficiently. This phenomenon can also result in a change in pressure near the inlet of the inducer and increase the amount of net positive suction head required [NPSHR] to make the pump continue to work efficiently or properly.
When the pressure of a liquid, such as a cryogenic fluid, falls below the vapor pressure, vapor bubbles will form in the fluid. As this liquid-vapor fluid combination is pumped through a machine, such as an inducer, impeller or pump, the fluid pressure increases. If the fluid pressure increases above the vapor pressure, the vapor bubbles in the fluid will collapse, which is called “cavitation.” It is desirable to prevent cavitation in devices because the collapsing bubbles can generate shock waves that are strong enough to damage moving parts around them. In addition, cavitation causes noise, vibration, and erosion of material from the device. Thus, the service life of a pump can be shortened due to cavitation.
However, it is desirable, when pumping cryogenic fluid from a tank to get the fluid pressure as close to the vapor pressure as possible, in order to pump more fluid from the tank. In other words, it is desirable for the net positive suction head available (NPSHA) in the tank to be greater than the net positive suction head required (NPSHR) of the pump. NPSHA is a function of the system in which the pump operates, such as the pressure of the fluid within a containment vessel or tank before it enters the inducer at the inlet of the pump, and the liquid depth of the vessel or tank housing the pump, among other factors.
The techniques used to improve pump performance relative to the operation of inducers vary significantly. For example, Nguyen Duc et al., U.S. Pat. No. 6,220,816, issued Apr. 24, 2001, describes a device for transferring fluid between two different stages of a centrifugal pump through use of a stator assembly that slows down fluid leaving one impeller before entering a second impeller. A different technique is used in Morrison et al., U.S. Pat. No. 6,116,338, issued Sep. 12, 2000, which discloses a design for an inducer that is used to push highly viscous fluids into a centrifugal pump. In Morrison et al., an attempt is made to resolve the problem of fluids rotating with the inducer blades by creating a very tight clearance between the blades of the auger of the inducer and the inducer housing, and configuring the auger blades in such a way as to increase pressure as fluid moves through the device to the pump.
While grooves have been used in inducer designs in the past, they have not been used to help efficiently move the fluid through the inducer. For example, in Knopfel et al., U.S. Pat. No. 4,019,829, issued Apr. 26, 1977, an inducer is illustrated that has a circumferential groove around a hub at the front of the inducer. This design causes turbulence to develop within the grooves of the inducer hub rather than in the fluid outside of the grooves, thereby reducing the tendency of the fluid to pulsate and generate noise.
Grooves are also illustrated and described in Okamura et al., An Improvement of Performance-Curve Instability in a Mixed-Flow Pump by J-Grooves, Proceedings of 2001 ASME Fluids Engineering Division, Summer meeting (FEDSM '01), May 29-Jun. 1, 2001, New Orleans, La. In Okamura et al., a series of annular grooves are formed on the inner casing wall of a mixed-flow water pump to suppress inlet flow swirl and therefore passively control the stability performance of the pump.
In particular, the J-grooves of Okamura et al. reduce the onset of back flow vortex cavitation and rotating cavitation that can be induced by the flow swirl at the inlet of the inducer.
Okamura et al. acknowledge, however, that increasing the specific speed of mixed-flow pumps has a tendency to make their performance curves unstable and to cause a big hump at low capacities, thus it is stated that it is doubtful that the illustrated technique would be effective for higher specific-speed, i.e., higher flow rate pumps.
Contra-rotating blade rows such as the stator 69 shown in FIG. 1E on or around a horizontal shaft 63 have been used for marine applications, specifically for propulsion of marine vessels. The goal in marine vessels is to improve aerodynamics and power generation. Most importantly, marine vessels generate and use high thrust forces in order to drive the marine vessels. Thus, maximizing thrust forces allows for faster and more powerful marine vessels.